Logarithm

A logarithm is an exponent. The properties of logarithms can be used to simplify computations that might otherwise be very long and cumbersome, but such computations are now usually carried out with calculators.

The exponential equation y = bx  can be equivalently expressed by the logarithmic equation logby = x, which can be read, "the logarithm to the base b of y is x." Because logarithms are exponent, they satisfy the same properties as exponents, including the following:
  1. logb(xy) = logbx + logby
  2. logb (x/y) = logbx - logby
  3. logb x2 = y logb x
  4. logb x1/y = (1/y) logb x
Any positive number other than one can be used as a base for a logarithm. The bases used most often are base 10 (because the ordinary number system uses base 10) and base e (e = 2.7182818284590), which simplifies many scientific calculations. Logarithm to base 10 are called natural logarithm. When common logarithms are used. It is customary to dispense with any mention of the base. For example, log 100 = 2 means that the logarithm to base 10 or common logarithm, of 100 is 2. In other words, 102=100. 

Each common logarithm has two parts, a characteristic and a mantissa. The characteristic is the number to the left greatest power of 10 that is less than the number whose logarithm is being found. The mantissa of the logarithm is the part that follows (is to the right of) the decimal point. It is normally determined by referring to a mathematical table of logarithm.

The discovery of logarithm (c.1614) is attributed to John Napier of Scotland and Jobst Birg) of Switzerland. Logarithmic table were developed in the early 1600s by Henry Briggs of England and Adrian Ulacq of the Netherlands.

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